2009 final -- solutions

2009 final -- solutions - FINAL EXAM STAT 101 Instructors A...

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FINAL EXAM STAT 101, Instructors: A. Wyner, A. Rakhlin December 15, 2009 Student Name: Section: Instructions Use the space provided to answer questions. You can use the back of these pages as scratch paper. You must show work and give explanations (except for the multiple-choice questions). Rules of uniformity: One-sided letter crib sheet, calculator ok (even with statistical functions and graphing), otherwise closed notes, closed book. No cell phones visible! Rules of Fairness: Complete this exam entirely on your own. Do not acquire information from other stu- dents or the outside in any form. Do not take copies of this exam out of this room. You have two hours for this exam. Any student observed continuing to write after time has been called will be documented and points will be deducted. Rules of Consideration: Be considerate to others by not causing commotion and distraction. If you finish early, leave quietly; avoid slamming doors. Honor code applies to the above Rules. Your signature: About this test: When more than one choice seems reasonable, pick the one that is best. STOP WAIT UNTIL YOU ARE INSTRUCTED TO PROCEED. 19 questions for a total of 100 points.
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STAT 101 Final Exam 1. (2 points) If the sample size n is large and p is the population proportion, the sampling distri- bution of the proportion is approximately (a) Binomial Bin (1 / 2 ,p ) (b) Normal N ( p,SD ( X i )) (c) Normal N ( p,p (1 - p ) /n ) (d) Normal N p, ˆ p (1 - ˆ p ) /n ) (e) Normal N ( p, p p (1 - p ) /n ) 2. (2 points) The Central Limit Theorem asserts that for i.i.d. random variables X 1 ,...,X n (a) The histogram of the data closely resembles the probability distribution of X i when n is large. (b) The histogram of the data closely approximates the mean of the population when n is large. (c) The sampling distribution of the mean is approximately normal when n is large. (d) The sampling distribution of the mean resembles the probability distribution of X i . 3. (2 points) The probability distribution for the average of 9 i.i.d. normal N (2 , 3 2 ) random variables X 1 ,...,X 9 is best described as (a) Approximately N (2 , 3 2 ) (b) Exactly N (2 , 3) (c) Exactly N (1 / 9 , 3 2 / 9) (d) Exactly N (2 , 1) (e) Can only be determined if the distribution of X i is known since the smaple size n is only 9. 4. (2 points) A sample of size 80 produces a confidence interval of length 2. To make the length of the interval equal to 1, we can (a) Increase sample size by an additional 4 points (84 total) (b) Change control limits to decrease Type I error (c) Decrease sample size by a factor of 4 (20 total) (d) Increase sample size by a factor of 4 (320 total) 5. (2 points) A given sample yields a 95% confidence interval [5 , 10] for the population mean μ . This means that
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2009 final -- solutions - FINAL EXAM STAT 101 Instructors A...

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